Ruffini-Horner Algorithm for Complex Arguments

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Suppose we need to calculate a value of the polynomial with real coefficients for the complex argument . We divide the polynomial by , where and . The remainder is then a linear function and the value of the polynomial is the value of the remainder. In the table, that is the value at the bottom right.


The table is defined as follows, where the last row is the sum of the higher rows:


Contributed by: Izidor Hafner (June 2017)
Open content licensed under CC BY-NC-SA



According to [1, p. 1034] this is called the Collatz contribution.


[1] D. Kurepa, Higher Algebra, Book 2 (in Croatian), Zagreb: Skolska knjiga, 1965.

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